Method for producing highly accurate frequency and FM of a laser

ABSTRACT

A method and apparatus for accurately and precisely controlling the frequency (wavelength) and periodic frequency modulation of a laser are provided. An ADC (Analog to Digital Converter) is used to sample the output of a modified interferometer used as a delay line discriminator, and quadrature components of the sampled output are generated. An arctangent function (e.g., atan2) is applied to convert the quadrature components to a phase measure that is proportional to the laser frequency. Correlator circuits (e.g., cost-efficient correlator circuits) are provided to extract average frequency, modulation peak deviation, and modulation phase error signals. Control-loop feedback using the extracted signals is used to adjust the average frequency, modulation deviation, and modulation phase to respective set points.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The invention relates generally to the field of modulating a frequencyor wavelength of electromagnetic waves, for example modulating laserfrequencies when range-finding.

2. Background Information

When a laser is used to determine range or distance to an object,accuracy of the determined range depends on how accurately or preciselythe light frequency or wavelength of the laser can be modulated.Accordingly, accurate and inexpensive methods for modulating laserfrequencies are desirable.

SUMMARY OF THE INVENTION

In accordance with exemplary embodiments of the invention, a method andapparatus are provided for accurately and precisely modulating thewavelength and phase of a laser. An ADC (Analog to Digital Converter) isused to sample the output of a delay line discriminator (e.g., aninteferometer) translated to an intermediate frequency (IF) carrier.Quadrature components of the sampled output are generated and anarctangent function (e.g., atan2) is applied to convert the quadraturecomponents to a phase measure that is proportional to the laserfrequency. Correlator circuits are provided to extract averagefrequency, modulation peak deviation, and modulation phase errorsignals. Control-loop feedback using the extracted signals is used toadjust the average frequency, modulation deviation, and modulation phaseto respective set points.

BRIEF DESCRIPTION OF THE DRAWINGS

Other objects and advantages of the present invention will becomeapparent to those skilled in the art from the following detaileddescription of preferred embodiments, when read in conjunction with theaccompanying drawings wherein like elements have been designated withlike reference numerals and wherein:

FIG. 1 shows a block diagram of a frequency modulation control of alaser, in accordance with an embodiment of the invention.

FIG. 2 shows a block diagram of a frequency modulation control of alaser, in accordance with an embodiment of the invention.

FIG. 3 shows an example of selected signals from operation of the deviceshown in FIG. 2.

FIG. 4 shows a power spectrum of an interferometer IF signal in anexperimental implementation of an embodiment of the invention.

FIG. 5 shows an instantaneous frequency measure from the interferometerin the experimental implementation of an embodiment of the invention.

FIG. 6 shows a corrected instantaneous frequency measure from theinterferometer in the experimental implementation of an embodiment ofthe invention.

FIG. 7 shows an interferometer frequency measurement error vs.integration time in the experimental implementation of an embodiment ofthe invention.

FIG. 8 shows a phase consistency as a function of integration time, inthe experimental implementation of an embodiment of the invention.

FIG. 9 shows a frequency measurement error vs. arctangent ROM size forthe experimental implementation of an embodiment of the invention.

FIG. 10 shows a block diagram of a frequency modulation control of alaser, in accordance with an embodiment of the invention.

FIG. 11 shows a block diagram of a frequency modulation control of alaser, in accordance with an embodiment of the invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

In accordance with the invention, a method is provided for generatinghighly stable and accurate sinusoidal frequency modulation (FM) of acontinuous wave (CW) laser. High accuracy is needed, for instance, whenemploying an FM-CW laser to determine range to a target.

In accordance with an exemplary embodiment of the present invention, ithas been found that it is not difficult to obtain highly linearmodulation characteristics, wherein the actual frequency modulationproduced is sinusoidal with very little distortion, when the appliedmodulation control signal (e.g., a voltage signal) is sinusoidal.Because of this, use of a sinusoidal modulation waveform allows one toproduce highly accurate frequency modulation by adjusting only twoparameters: 1) modulation depth (FM deviation, e.g. peak deviation fromthe center frequency), and 2) modulation phase (e.g., a phase differencebetween the modulation control signal and the signal being modulated).For some laser rangefinders, measurement accuracy of these twoparameters should be better than 0.1% for measured peak-to-peak FMdeviation, and 0.1 degrees for measured absolute modulation phase.

In accordance with an exemplary embodiment of the invention, a controldevice for accurately modulating the frequency of a CW laser includes adelay-line interferometer for sampling the CW laser. The delay-lineinterferometer includes a frequency-offset in one or both legs of theoptical path of the interferometer. The frequency offset can, forexample, be generated using one or more acousto-optical modulators(AOMs). The control device also includes an intermediate frequencyprocessor (e.g., an amplifier and a bandpass filter) along with anAnalog-to-Digital Converter (ADC), for filtering and then converting theoutput of the interferometer. The control device includes a digitalquadrature module that receives the output of the ADC and generates orextracts quadrature components having highly accurate amplitude andphase balance. The control device further includes an arctangentfunction module (e.g., a lookup table in ROM or RAM), that converts thequadrature components from the digital quadrature module to a phasemeasure that is proportional to the laser frequency. Correlator circuitsare also included in the control device. The correlator circuits extractinformation from the phase measure such as modulation peak deviation,average frequency of the laser, and modulation phase error. Theinformation extracted by the correlator circuits is used to control themodulation of the laser so that the amplitude and phase of themodulation are correct.

FIG. 1 shows an exemplary laser receiver and control circuit inaccordance with the invention. A laser transmitter 106 isfrequency-modulated via a piezoelectric transducer (PZT) 107, and amodulation generator 104 controls the PZT 107. An RF source 102 is alsoconnected to the laser transmitter 106 to supply power to excite thelaser. The mirror 108 is used to sample the output of the lasertransmitter 106, and the mirrors 110, 114 direct laser light returningfrom a target to a detector 128 connected to a first module 127 ofamplifiers and filters, for the purpose of determining a range to thetarget. The mirror 112 also directs a portion of the sampled output ofthe laser, to the detector 128 for purposes of determining the range tothe target. The mirror 116 splits the remaining portion of the sampledoutput of the laser in two, and directs the first part to a firstacousto-optic modulator (AOM) 136, while allowing the second, remainingpart to pass through the mirror 116 and enter an optical delay path 140composed of spaced mirrors 120, 122, 118.

A delay τ provided by the optical delay path 140 is proportional to thelength of the path, where τ=L/c where L is the path length, and c is thespeed of light through the path.

After passing through the optical delay path 140, the second part isdirected to a second AOM 138. Laser light emerging from the AOMs 136,138 is directed to a detector or mixer 132 via mirrors 124, 126. Anoutput signal of the detector 132 is provided to a second module 130 ofamplifiers and filters, and the output of the second module 130 isultimately used to control the modulation of the laser transmitter 106.A digital synthesizer 134 provides reference signals for use within thesystem, for example by the AOMs 136, 138.

In particular, the second detector 132 in FIG. 1 produces a heterodyneof the un-delayed, shifted laser signal

a·cos([ω_(laser)−ω₁]t)   (1)

and the delayed, shifted signal is

a·cos([ω_(laser)−ω₂](t−τ)−Ψ)   (2)

where the AOMs 136, 138 perform the shifts by ω₁ and ω₂ respectively,and where τ is the delay imposed by the optical delay path. The phaseangle Ψ represents a phase angle due to phase shifts in hardware and theexact length of the optical paths. It can be considered to be stable,but not set to any particular value.

We will consider that the AOMs 136, 138 shift the optical frequency downby f₁ or f₂ and that f₁>f₂. Thus we define a positive

f _(IF) =f ₁ −f ₂   (3)

The “Interferometer Output for FM Monitoring” of FIG. 1 is then$\begin{matrix}{{x(t)} = {a^{2} \cdot {\cos \left( {{\left\lbrack {\omega_{laser} - \omega_{2}} \right\rbrack \cdot \left( {t - \tau} \right)} - \Psi - {\left\lbrack {\omega_{laser} - \omega_{1}} \right\rbrack \cdot t}} \right)}}} & (4) \\{\quad {= {a^{2} \cdot {\cos \left( {{\omega_{IF} \cdot t} - {\omega_{L} \cdot \tau} - \Psi} \right)}}}} & (5)\end{matrix}$

where ω_(IF)=2πf_(IF) and ω_(L)=ω_(laser)−ω₂

We can also write

x(t)=Re(X·e ^(J) ^((ω) ^(_(IF)) ^(t)) )   (6)

where

X=a ² ·e ^(−J(ω) ^(_(L)) ^(·τ+Ψ))   (7)

We can sample the signal x(t) at 4 times the IF frequency (f_(IF)) ofsampling by forming the I(n) samples from consecutive even samples andthe Q(n) samples from consecutive odd samples thusly: ${{\begin{matrix}{{I(n)} = \quad {{x\left( {\left\lbrack {4 \cdot n} \right\rbrack \cdot T} \right)} - {x\left( {\left\lbrack {{4 \cdot n} + 2} \right\rbrack T} \right)}}} & {\quad (8)} \\{{= \quad {{Re}\left( {{X \cdot ^{j^{({{\omega_{IF}{\lbrack{4 \cdot n}\rbrack}}T})}}} - {X \cdot ^{j^{({{\omega_{IF}{\lbrack{{4 \cdot n} + 2}\rbrack}}T})}}}} \right)}}\quad} & {\quad (9)} \\{= \quad {{Re}\left( {{X \cdot ^{j^{({2\pi \quad n})}}} - {X \cdot ^{j^{({{2\pi \quad n} + \pi})}}}} \right)}} & {\quad (10)} \\{= \quad {2a^{2}{\cos \left( {{\omega_{L}\tau} + \Psi} \right)}}} & {\quad (11)}\end{matrix}{and}\quad \begin{matrix}{\left. {{Q(n)} = \quad {{x\left( \left\lbrack {{4 \cdot n} + 1} \right. \right)}T}} \right) - {x\left( {\left\lbrack {{4 \cdot n} + 3} \right\rbrack T} \right)}} & {\quad (12)} \\{= \quad {{RE}\left( {{X \cdot ^{j^{({\omega_{IF}{\lbrack{{4 \cdot n} + 1}\rbrack}})}}} - {X \cdot ^{j^{({{\omega_{IF}{\lbrack{{4 \cdot n} + 3}\rbrack}}T})}}}} \right)}} & {\quad (13)} \\{= \quad {{Re}\left( {{X \cdot ^{j^{({{2\pi \quad n} + \frac{\pi}{2}})}}} - {X \cdot ^{j^{({{2\pi \quad n} + \frac{\pi}{2} + \pi})}}}} \right)}} & {\quad (14)} \\{= \quad {{Re}\left( {j \cdot 2 \cdot X} \right)}} & {\quad (15)} \\{= \quad {- {{Im}\left( {2 \cdot X} \right)}}} & {\quad (16)} \\{= \quad {2{a^{2} \cdot \sin}\quad \left( {{\omega_{L} \cdot \tau} + \Psi} \right)}} & {\quad (17)}\end{matrix}\text{where}\quad T} = {{\frac{2\pi}{4 \cdot \omega_{IF}}\quad \text{(}\text{i.e.,~~sample~~rate}} = {{4 \cdot f_{IF}}\text{)}}}}\quad$

Now we can derive our estimate of the (instantaneous) laser frequency as$\begin{matrix}{{f_{est}(n)} = \quad {{\left( \frac{1}{2{\pi \cdot \tau}} \right) \cdot a}\quad \tan \quad 2\left( {{Q(n)},{I(n)}} \right)}} & {\quad (18)} \\{= \quad {{\left( \frac{1}{2{\pi \cdot \tau}} \right) \cdot a}\quad \tan \quad 2\left( {{2a^{2}\sin \quad \left( {{\omega_{L} \cdot \tau} + \Psi} \right)},{2a^{2}{\cos \left( {{\omega_{L} \cdot \tau} + \Psi} \right)}}} \right)}} & {\quad (19)} \\{= \quad {\left( \frac{1}{2{\pi \cdot \tau}} \right) \cdot \left( {{\omega_{L} \cdot \tau} + \Psi + {2\pi \quad p}} \right)}} & {\quad (20)} \\{= \quad {f_{L} + f_{amb}}} & {\quad (21)}\end{matrix}$

where atan2 is the four quadrant arctangent function,

where $\begin{matrix}{f_{L} = \frac{\omega_{L}}{2\pi}} & (22)\end{matrix}$

and where the 2π·p ambiguity and the unknown Ψ contribute to theunknown, but stable frequency ambiguity: $\begin{matrix}{f_{amb} = {\frac{\Psi}{2{\pi \cdot \tau}} + \frac{p}{\tau}}} & (23)\end{matrix}$

(where p is an integer)

Usually we do not need to know f_(L) unambiguously, but rather, we wouldlike to stabilize it through a control loop that uses any variations asfeedback. If unambiguous measurement of f_(L) is desired, other means(such as knowing the possible laser emission frequency limits) may beused to resolve the approximate integer p. The ambiguous interval offrequency is 1/τ. For example, if a 4-meter delay line were used, theinterval would be 75 MHZ.

Even if the laser frequency is modulated, the foregoing derivation is agood approximation for most applications. Assuming sinusoidal FM of thelaser,

f _(L)(t)=f ₀ −f ₂ +Δf·cos(ω_(m) ·t+θ _(m))   (24)

where Δf is the peak deviation,

f₀ is the laser center frequency,

ω_(m)=2πf_(m) is the frequency of the sinusoid, and

θ_(m) is the phase angle of the modulation

We can design the modulation to be synchronous to the IF frequency,i.e., so that the modulation period is a multiple M of the IF period:$f_{m} = {{\frac{1}{M \cdot 4 \cdot T}\quad \omega_{m}} = \frac{2\pi}{4 \cdot M \cdot T}}$

The average frequency of the laser is obtained by averaging the measuredfrequency over exactly one cycle (with exactly M samples per cycle). Mcan be, for example, an integer multiple of 4. Note that I(n)+jQ(n) issampled at a sampling interval of 4·T, or with a sampling frequency off_(IF) since $T = {\frac{2\pi}{4 \cdot \omega_{IF}}.}$

Thus, average frequency can be obtained in the following fashion:$\begin{matrix}{f_{ave} = \quad {\frac{1}{M} \cdot {\sum\limits_{n = 0}^{M - 1}{f_{est}(n)}}}} & {\quad (25)} \\{= \quad {\frac{1}{M} \cdot {\sum\limits_{n = 0}^{M - 1}\left( {f_{amb} + f_{L}} \right)}}} & {\quad (26)} \\{{= \quad {f_{0} + f_{amb} - f_{2} + {\frac{\Delta \quad f}{M} \cdot {\sum\limits_{n = 0}^{M - 1}{\cos \left( {{\frac{2\pi}{4{MT}} \cdot {n4T}} + \theta_{m}} \right)}}}}}\quad} & {\quad (27)} \\{= \quad {f_{0} + f_{amb} - f_{2}}} & {\quad (28)}\end{matrix}$

Note that the last term of equation (27) is identically zero, yieldingequation (28). Thus, f_(ave) is the measure of the laser centerfrequency f₀, offset by fixed ambiguity of f_(amb)−f₂.

With respect to obtaining a measure of peak deviation, assuming we use acontrol loop to control the modulation phase to be very close toθ_(M)=0, we can form the square-wave weighted sum of samples off_(est)(n). For simplicity we will illustrate integration over a singlemodulation period, as shown below in equations (29)-(32).

The first M/2 samples will be weighted by the +1 value of the squarewave, while the second M/2 samples will be weighted by the −1 value ofthe square wave (wherein, for example, the square wave is the Phase 1square wave generated by the function generator 284 shown in FIG. 2).$\begin{matrix}{S_{dev} = \quad {{\sum\limits_{n = 0}^{\frac{M}{2} - 1}{f_{est}(n)}} + {\left( {- 1} \right) \cdot {\sum\limits_{n = \frac{M}{2}}^{M - 1}{f_{est}(n)}}}}} & {\quad (29)} \\{= \quad {{\sum\limits_{n = 0}^{\frac{M}{2} - 1}\left( {f_{0} - f_{2} + f_{amb} + {\Delta \quad {f \cdot {\cos \left( {\frac{2\pi}{4{MT}} \cdot n \cdot 4 \cdot T} \right)}}}} \right)} -}} & \quad \\{\quad {\sum\limits_{n = \frac{M}{2}}^{M - 1}\left( {f_{0} - f_{2} + f_{amb} + {\Delta \quad {f \cdot {\cos \left( {\frac{2\pi}{4{MT}} \cdot n \cdot 4 \cdot T} \right)}}}} \right)}} & {\quad (30)} \\{= \quad {{\sum\limits_{n = 0}^{\frac{M}{2} - 1}\left( {f_{0} - f_{2} + f_{amb} + {\Delta \quad {f \cdot {\cos \left( {\frac{2\pi}{4{MT}} \cdot n \cdot 4 \cdot T} \right)}}}} \right)} -}} & \quad \\{\quad {\sum\limits_{k = 0}^{\frac{M}{2} - 1}\left( {f_{0} - f_{2} + f_{amb} + {\Delta \quad {f \cdot {\cos \left( {{\frac{2\pi}{4{MT}} \cdot k \cdot 4 \cdot T} + {\frac{2\pi}{4{MT}} \cdot \frac{M}{2} \cdot 4 \cdot T}} \right)}}}} \right)}} & {\quad (31)} \\{= \quad {\Delta \quad f{\sum\limits_{k = 0}^{\frac{M}{2} - 1}{2\cos \quad \left( \frac{2\pi \quad k}{M} \right)}}}} & {\quad (32)}\end{matrix}$

Where in the second summation of equation (31), we have made the changeof variables $k = \left( {n - \frac{M}{2}} \right)$

From this, we deduce our estimate of peak FM deviation as${{\Delta \quad f} = \frac{S_{dev}}{K_{0}}},\quad {{\text{where}\quad K_{0}} = \quad {= {2 \cdot {\sum\limits_{k = 0}^{\frac{M}{2} - 1}{\cos \left( \frac{2\pi \quad k}{M} \right)}}}}}$

Phase error is derived in a similar fashion to the derivation of peakdeviation, but derives error that (for small angles) is proportional toθ_(m). Based on the foregoing descriptions, those ordinarily skilled inthe art can easily derive the phase error, and thus the derivation isnot reproduced here. The phase error is used to close the loop thatkeeps θ_(m)≈0.

In summary, the computed frequency estimate can be used to monitor thefrequency deviation and phase shift of the FM modulation of the laser,for example in each of one or more ranging modes when the laser is usedin a rangefinding device. The estimates of these parameters will be usedto accurately adjust the modulation parameters to those assumed by therange processing algorithm implemented in the rangefinding device. Suchalgorithms are well known in the art of rangefinding. The frequencymeasure thus produced is then processed in three different ways.

First, the signal is integrated over an exact integer number ofmodulation cycles (when modulating) or for a preset interval of samples(when no modulation is present). The resulting signal is a measure ofthe average frequency of the laser, and can be used as feedback in asecond-order control loop to stabilize the laser center frequency.

Second, the signal is multiplied by a square wave that will be 90degrees out of phase with the FM modulation when the modulation phase isproperly adjusted. The product is then integrated for an exact integernumber of modulation cycles. The “multiplication” can be accomplished bychanging the sense of the digital integrator, rather than using adigital multiplier. In other words, multiplication of the signal by asquare wave can be accomplished using accumulators (integrators) ratherthan multipliers, thus reducing circuit complexity and powerconsumption. Since the square wave for purposes of the multiplication isbinary and has either a value of either +1 or −1, multiplying the signalby the square wave and then integrating (accumulating) the result is thesame as multiplying the current sample of the signal by +1 or −1 (theinstant value of the square wave) and then adding the result to thecumulative total (of multiplied sample values). This can be done, forexample, by applying the square wave to the add/subtract input of theaccumulator, and applying the signal samples to the accumulator. Theresult from the integrator/accumulator will be an error signal thatnulls when the phase of the laser is properly adjusted. Note thatmultiplication of the signal by a sine wave of the same period as theabove-mentioned square wave, instead of by the square wave, would beslightly preferable from a noise and spurious signal susceptibilitypoint of view, but would require an actual digital multiplier, whichwould add to the complexity (and likely also the power requirements) ofthe implementation. This refinement may be unnecessary to achievedesired or required accuracy in most applications.

Third, the signal is also multiplied by a square wave that will bein-phase with the FM modulation when the processing described above (ofintegrating the signal over an exact integer number of modulation cyclesor for a preset interval of samples, to obtain the average frequency ofthe laser), has properly aligned the modulation phase. This product isalso integrated as in the process of obtaining the average frequency ofthe laser, but the result is proportional to the peak-to-peak frequencymodulation. The result is scaled to a deviation estimate that issubtracted from a set-point deviation to produce an error signal. Thiserror signal closes a second-order loop to correct the frequencydeviation of the FM modulation. Multiplication of the signal with thein-phase square wave and integration of the result can be accomplishedin the same fashion as described above with respect to the out-of-phasesquare wave (e.g., by applying the square wave to the Add/Subtract inputof an accumulator). In addition, the same principles noted above apply,when considering the viable alternative of using a sine wave instead ofthe square wave.

Note that the coefficients of processing to obtain the estimate of phaseestimate and the estimate of deviation of the FM modulation, describedfor example in the immediately preceding paragraphs, depend on themodulation frequency. The average frequency loop, or estimation ofaverage frequency, does not change with modulation, so long as theintegration period is an integer multiple of the modulation period whenthe modulation is present.

Those of ordinary skill in the art will also recognize that theintegration (or accumulation) time can be appropriately selected. At theend of this time, one or more corrections is applied and the time isreset and the integration begun anew. The longer the integration time,the more accurate the estimates. However, the stability of the lasermust also be considered. The less stable the laser, the more frequentlyit will need to be corrected. Thus, the accuracy of each correction mustbe balanced against a desirable or necessary frequency of correction(e.g., how often corrections are applied). This of course will depend onthe practical details of specific implementations, for example thespecific laser being used, and can be easily determined by those ofordinary skill in the art.

An example implementation of a laser frequency and FM control device inaccordance with exemplary embodiments of the present invention, is shownin FIG. 2. FIG. 2 shows a laser 106 with a PZT (Piezo-ElectricTransducer) 107 that modulates the wavelength of the laser. A samplefrom the output of the laser 106 having a frequency f is provided toAOMs (Acousto-Optical Modulators) 136, 138 which are respectivelymodulated with input frequency signals f₁, f₂. The output of the AOM136, which will have a frequency equal to f−f₁, is provided to adetector/mixer 242. The output of the AOM 138, which will have afrequency equal to f−f₂, is provided to a delay 240 that delays thesignal by a time ΔT. The delayed signal from the delay 240 is alsoprovided to the detector/mixer 242. The detector/mixer 242 outputs themixed signal to a BPF (BandPass Filter) 244, which is centered onf_(if)=f₁−f₂. The output of the BPF 244 is provided to an ADC (Analog toDigital Converter) 246 which samples the output of the BPF 244 at a rateequal to 4·(f₁−f₂). The resulting samples are output from the ADC 246 toa Quadrature Development module 256 that generates quadrature signalsI(n), Q(n) based on the signal samples from the ADC 246. The quadraturesignals are provided from the module 256 to an atan2 module 258 thatreceives the quadrature signals and applies them as a dual-argumentoperand for the atan2 function, which is a 4-quadrant arctangentfunction well known in the art (e.g., atan2(Q, I)). The resulting value,f_(est)(n), is provided (properly scaled) from the module 256 to each ofthree accumulators, 260, 262, 264.

The accumulator 260 also receives, at its Add/Subtract input, a Phase 1square wave signal from the function generator 284. The Phase 1 squarewave signal is generally in phase with the FMX signal, as can be seen byinspection of the function generator 284 as shown in FIG. 2. The FMXsignal is a frequency modulation excitation voltage.

The accumulator 264 also receives, at its Add/Subtract input, a Phase 2square wave signal from the function generator 284. The Phase 2 squarewave signal is generally 90 degrees out of phase with the FMX signal, ascan be seen by inspection of the function generator 284 as shown in FIG.2.

Each of the accumulators 260, 262, 264 also receives, at a reset input,an Accum signal from the function generator 284. The Accum signal resetsthe accumulators when the accumulation or integration period iscompleted, so that a new period will begin.

The output of the accumulator 260 is proportional to the frequencydeviation of the signal, S_(dev)=K₀·Δf. The output of the accumulator262 is proportional to the mean frequency, f_(ave)·M.

The Accum signal is also applied to clock inputs of D flip flop circuits266, 268, 270 that are respectively connected to the outputs of theaccumulators 260, 262, 264, to register the accumulation/integrationresults at the end of an accumulation time interval, and transfer theseresults to the outputs of the D flip flop circuits 266, 268, 270. Theoutputs of the D flip flop circuits 266, 268, 270 are respectivelyapplied to multipliers 272, 274, 276, that multiply the outputsrespectively by the factors K₃, K₁, K₂.

The output of the multiplier 272 is subtracted from a deviation setpointor set value in a summer 278, to generate a deviation error signal thatis fed back to an integrator 254. The output of the integrator 254 isapplied to a multiplier 250 to change or adjust the modulation of thelaser 106 by the FMX output of the function generator 284.

The output of the multiplier 274 is subtracted from a frequency setpointor set value in a summer 280, to generate a frequency error signal thatis fed back to an integrator 252 and applied via the adder 248 to thePZT 107 to change or adjust the center frequency of the laser 106.

Specifically, the output of the integrator 254 is multiplied with the FMmodulation signal output from the function generator 284, in amultiplier 250, and the result is then added to the output of theintegrator 252 in an adder 248. The final result from the adder 248 issupplied to the PZT 107.

The output of the multiplier 276 represents the phase offset, and issupplied to an integrator 282 whose output is fed to the functiongenerator 284. The function generator uses the integrated phase offsetsignal from the integrator 282 to shift the phase of the FMX excitationsignal to the Phase 1, Phase 2, and Accum signals. The Phase 1 and Phase2 signals are always 90 degrees out of phase with each other.

The common clock signal provided to the function generator 284 can havea frequency equal to (f₁−f₂), which is thus an exact multiple of themodulation frequency f_(m).

The feedback loops shown in FIG. 2 are type-II loops, so that thereshould be no steady-state frequency error in the absence of significantdrift characteristics, and so that linear drift characteristics can bereduced to the required level by adjusting the loop gain.

FIGS. 10-11 show embodiments similar to the embodiment shown in FIG. 2,but which have one AOM instead of two AOMs. Ordinarily, f₁ and f₂ arechosen so that the difference (f₁−f₂) is a desired value, for example, 1megahertz. When only one AOM is provided, and is supplied with an inputfrequency signal f, the difference is effectively f−0=f. Thus, when oneAOM is used, the input frequency signal f that is supplied to the AOMshould be equal to the desired value. FIG. 10 shows an embodiment whereonly one AOM 1138 is provided, and is connected to the delay 240. FIG.11 shows another embodiment where only one AOM 1136 is used, connecteddirectly between the laser output sample and the detector/mixer 242. Inthe embodiments shown in FIGS. 10-11, the ADC 246 preferably samples at4·f where f is the frequency input to the single AOM 1136, 1138. Thoseof ordinary skill in the art will recognize that the frequencies f₁, f₂of FIG. 2 and the frequency f of FIGS. 10-11 can be appropriatelyselected, based on circumstances of a particular application and onavailable resources and components (e.g., available AOMs).

FIG. 3 shows a real world example, where the actual frequency of thelaser, f_(laser) is controlled to be in phase with the square wave Phase1, and 90 degrees out of phase with the square wave Phase 2. The FMXsignal output from the function generator 284 is also shown, slightlyadvanced with respect to the laser frequency f_(laser) by an amountcorresponding to the phase control input signal received from theintegrator 282. Typically the laser will lag a little.

The signals Phase 1, Phase 2, Accum, and FMX in the function generator284 can be generated by using at least one counter that receives theclock signal, and outputs addresses in a ROM (Read Only Memory) thatcontains values for points on the curves of the periodic signals Phase1, Phase 2, and FMX. In other words, the ROM can have sequential signalvalues located in sequentially addressed memory locations, so that theoutput of the counter can be used to generate the sequential addressesand access the corresponding signal values. Phase of a periodic signalcan be adjusted adding an appropriate offset to the counter value/memoryaddress. Of course, other appropriate techniques well known in the artof function generation can additionally or alternatively be used.

A description of an experimental implementation follows, with referenceto FIGS. 4-9. Interferometer data with the following characteristics wasused to successfully verify that adequate estimates of thepeak-deviation and phase-shift characteristics of the modulation can bederived. The laser wavelength was 11.15 micrometers, the IF frequencywas 1.25 Megahertz, the sampling frequency was 25 Megahertz (5-timesoversampled-5 Megahertz required), with a carrier-to-noise ratio greaterthan 50 dB in 300 Hz bandwidth after the detector, using a 5 Megahertzlow-pass filter. The number of samples was 13,000. The target modulationwas 4.6 kilohertz modulation frequency with 700 kilohertz peakdeviation.

The interferometer setup was similar to that shown in FIG. 1, exceptthat the frequencies f₁, f₂ and the IF frequency were not all phaselocked together. Instead, they were adjusted to be as close as possiblemanually using separate signal generators. The laser also was found tohave significant frequency drift when operating it without closed-loopfrequency stabilization. FIG. 4 shows the IF signal power spectrum,indicating that a good SNR was obtained. Because the modulation index ofthe laser is extremely high (greater than 150) the discriminatorfrequency measure should have a high SNR. In fact, the majority of thenoise present is due to the noise of the A/D converter used to samplethe IF signal. The figure shows the 1.25 megahertz carrier and itssecond and third harmonics. Since this is the signal after thephase/frequency differencing produced by the mixer/detector, the phasemodulation is very low-index at this point and cannot be seen on thisscale in the power spectrum.

The frequency measure (the scaled arctangent result) is plotted in FIG.5, showing a relatively large amount of laser frequency drift over ashort (4 millisecond) time period. (This amount of drift would beexcessive in a well-designed laser). The drift was estimated from thedata in a piecewise linear fashion and then subtracted to give the morereasonable frequency measure (more typical of a well-designed system)shown by FIG. 6. This signal was then processed according to thealgorithm demonstrated in FIG. 2 for integration times from about 0.2 to3.6 milliseconds. The results are shown in FIG. 7. If longerintegrations times are or can be used, the errors can be systematicallyreduced as the square root of the integration time. Phase consistency islikewise shown in FIG. 8.

Finally, to ensure that the implementation is practicable, thequantization of the arctangent function was simulated, as would occur iflookup tables in ROM or RAM (Random Access Memory) were used to storethe function. FIG. 9 indicates that the use of 20 bits of address (10bits for each of I and Q) appears to be quite adequate, allowing the useof a 1-Meg word memory (with 2 bytes per word). Reviewing FIG. 2, onesees that the processing can be implemented very efficiently using avery reasonable amount of readily availabe digital hardware.

It will be appreciated by those skilled in the art that the presentinvention can be embodied in other specific forms without departing fromthe spirit or essential characteristics thereof, and that the inventionis not limited to the specific embodiments described herein. Thepresently disclosed embodiments are therefore considered in all respectsto be illustrative and not restrictive. The scope of the invention isindicated by the appended claims rather than the foregoing description,and all changes that come within the meaning and range and equivalentsthereof are intended to be embraced therein.

What is claimed is:
 1. An apparatus for modulating the frequency andphase of a laser, comprising: a delay-line inteferometer for samplingthe laser, the interferometer including a frequency offset in at leastone leg of the optical path of the interferometer; an intermediatefrequency processor for filtering and converting the output of theinterferometer; a quadrature module for receiving an output of theintermediate frequency processor, and extracting quadrature componentsfrom the received output; an arctangent function module connected toconvert the extracted quadrature components to a phase measure that isproportional to the frequency of the laser; a plurality of correlatorcircuits connected to extract a modulation peak deviation, an averagefrequency of the laser, and a modulation phase error from the phasemeasure; and at least one feedback loop for controlling the laser basedon the extracted modulation peak deviation, the extracted averagefrequency of the laser, and the extracted modulation phase error.
 2. Theapparatus of claim 1, further comprising at least one acousto-opticmodulator for generating the frequency offset.
 3. The apparatus of claim1, wherein the intermediate frequency processor outputs a digital signalto the quadrature module, and the quadrature module is a digitalquadrature module.
 4. The apparatus of claim 1, further comprising afunction generator for generating first and second reference signals,wherein the first reference signal is 90 degrees out of phase with thesecond reference signal, the first reference signal is provided to afirst one of the plurality of correlator circuits, and the secondreference signal is provided to a second one of the plurality ofcorrelator circuits.
 5. The apparatus of claim 1, wherein the first andsecond reference signals are square waves, and wherein the first andsecond reference signals are connected respectively to add/subtractinputs of the first and second ones of the plurality of correlatorcircuits.